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MHT CET202521 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

The line of intersection of the plane r (3 i - j + k )=1 and r ( i +4 j -2 k )=2 is parallel to the vector

Options

  1. A2 i +7 j +13 k
  2. B-2 i -7 j +13 k
  3. C-2 i -7 j -13 k
  4. D-2 i +7 j +13 k

Correct answer

D. -2 i +7 j +13 k

Step-by-step solution

The line of intersection of two planes is perpendicular to both normal vectors, so its direction vector is parallel to the cross product n₁ n₂ . Given plane normals n₁ = 3 i - j + k and n₂ = i + 4 j - 2 k , compute: n₁ n₂ = vmatrix i & j & k 3 & -1 & 1 1 & 4 & -2 vmatrix = i ((-1)(-2) - (1)(4)) - j ((3)(-2) - (1)(1)) + k ((3)(4) - (-1)(1)) = i (2 - 4) - j (-6 - 1) + k (12 + 1) = -2 i + 7 j + 13 k This vector matches option D . D

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